Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987a%26a...179...80s&link_type=abstract
Astronomy and Astrophysics, Vol.179, NO.1/2JUN(I), P. 80, 1987
Astronomy and Astrophysics
Astrophysics
35
Scientific paper
The influence of gravitational light focussing caused by stars in a foreground galaxy on the observed luminosity function and surface number density is investigated. In a previous paper (Schneider, 1987 a, hereafter Paper 1) I have determined the amplification probability distribution (APD) for high amplification factors by taking into account the finite size of a source and the distortion of the gravitational field of a star by the galactic field (the so-called Chang-Refsdal lens model). Here, the APD for small (>1) amplifications is determined by considering an ensemble of stars acting on a light bundle simultaneously, together with the galactic gravitational field, which is characterized by the dimensionless shear parameter γ. Since the deflection angle near a star behaves like (impact parameter)-1, any background source causes a large number of (unresolvable) very faint images near the individual stars. The probability distribution for this "diffuse" flux component is determined, which is then combined with the strong and weak amplification results to yield the APD for all amplification factors > 1. Convolving this with unlensed source counts (USC) of sources, one obtains the observed source counts (OSC) and the number density enhancement of sources near galaxies. Using the final APD, the number density enhancement δN of sources near foreground galaxies is determined (see Fig. 3); in the inner part of the galaxy, δN depends on the local shear γ as well as on the source size b and the slope of the assumed USC. For γ < b, δN becomes independent of γ. If the logarithmic slope of the differential USC is flatter than -2, δN is negative. Applying these results to the observed quasar-galaxy-associations, where the area searched for QSOs around galaxies is quite large (several arcmin2), it is found that for isothermal galaxy models the galactic shear γ is rather unimportant, in spite of its influence on δN in the inner parts of galaxies. Excluding these regions, δN/N is proportional to the inverse of the angular distance from the center of the galaxy, the constant of proportionality being sensitively dependent on the source size and the form of the USC. Although the fractional number density enhancement of sources near galaxies may be considerably high, a huge sample of galaxies has to be investigated to isolate this effect from statistical noise. This conclusion, however, depends on the assumption that the luminosity function of quasars flattens for sources fainter than 21 mag, as suggested by observations. Finally, the amplification probability distribution is applied to the unique gravitational lens case 2237+0305 (Huchra et al., 1985).
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